Teachers' Considerations on the Irrationality Proof of $\sqrt{2}$

Abstract

In this article, we offer considerations of a group reflection on the analysis of the errors committed in an activity proposed to teachers who are enrolled in a professional master's degree in mathematics. The discussion is related to a mathematical content that is taught in the basic school and to the manifestation of the subjects regarding their responses to a certain activity. In this research, of a qualitative character, the instruments of data collection were the subjects' textual production, the observations made by the authors and annotated in a field diary, as well as an online questionnaire. As theoretical contribution,we made use of methodologies that emerge from the Error Analysis theory, aiming to classify the errors committed for further discussion and reflection in the group. The results indicate that the participants perceived as relevant the carried-out reflection, because they expressed the recognition that it is fundamental for the teacher to take into account the students' mistakes in their classroom activities. The fragility of the argumentation in mathematics among these teachers was verified as well, and this reinforces the need for these professionals to embrace in-service teachers' education.

Keywords:
Mathematical Knowledge; Error Analysis; Group Reflection; In-service Teachers-Education